https://thoughtstreams.io/combined/response-to-dave-about-principal-ideals/Response to Dave about Principal IdealsDavejtauber2016-08-24T07:02:33Zhttps://thoughtstreams.io/combined/response-to-dave-about-principal-ideals/#card-10778> What's particularly neat about this...2016-08-16T18:20:35Z2016-08-16T18:20:35ZDave
> What's particularly neat about this is I can construct a pyramid of interests so [the foundation is fairly broad ... and narrows to the specialization](https://thoughtstreams.io/jtauber/journeyman-of-some/10772/) I'm interested in as you go up.
James, may we risk saying that **cosmology** generates one of your **principal ideal**s?
https://thoughtstreams.io/combined/response-to-dave-about-principal-ideals/#card-10779Well, the irony is ring theory isn't ...2016-08-16T18:22:31Z2016-08-16T18:22:31Zjtauber
Well, the irony is ring theory isn't part of the constructed background of interests for cosmology :-)
https://thoughtstreams.io/combined/response-to-dave-about-principal-ideals/#card-10793Actually, I'm wrong, my constructed b...2016-08-19T03:40:34Z2016-08-19T03:40:34Zjtauber
Actually, I'm wrong, my constructed background *does* include the course "Groups, Rings and Modules" at Cambridge.
https://thoughtstreams.io/combined/response-to-dave-about-principal-ideals/#card-10794BTW, huge points to [Dave](https://th...2016-08-19T03:41:37Z2016-08-19T03:41:37Zjtauber
BTW, huge points to [Dave](https://thoughtstreams.io/Dave/) for suggesting the light-cone as a more useful analogy in the context of cosmology.
https://thoughtstreams.io/combined/response-to-dave-about-principal-ideals/#card-10795if speaking in terms of [Principal Id...2016-08-19T03:41:51Z2016-08-19T03:41:51ZDave
if speaking in terms of [Principal Ideals](https://thoughtstreams.io/jtauber/response-to-dave-about-principal-ideals/) is inconsistent, we could always press the cosmological background-cone into service.
Consider the interval between, eg **cosmology**, and any other concept: we can classify these intervals according to the following schema:
- consequential: one background cone contains the other.
- inconsequential: the background cones fail to intersect, or do so only partially.
- tangential: one concept occurs on the boundary of the other's background cone.
I hope a trichotomous classification of intervals *is* consequential with regard to cosmology? :-)
https://thoughtstreams.io/combined/response-to-dave-about-principal-ideals/#card-10796I love the idea of saying that, for e...2016-08-19T03:46:35Z2016-08-19T03:46:35Zjtauber
I love the idea of saying that, for example, "Vector Calculus is in the past light-cone of cosmology".
To more precisely relate his trichotomy to light-cones, I think you have:
* subject A is in the past light-cone of subject B
* subject A and B both have subject C in their past light-cone
* subject A and subject B are space-like
https://thoughtstreams.io/combined/response-to-dave-about-principal-ideals/#card-10805I'd intended the [trichotomy](https:/...2016-08-24T07:01:57Z2016-08-24T07:01:57ZDave
I'd intended the [trichotomy](https://thoughtstreams.io/jtauber/response-to-dave-about-principal-ideals/10796/) to be:
- consequential / timelike
- inconsequential /spacelike
- tangential / lightlike
but it's been decades since I've dealt with the [molluscs](https://thoughtstreams.io/Dave/embalmed-ones/10804/) of space-time.